The regime decides it before anything else
Before working out which deductions you qualify for, check which regime you are on, because it can make the whole question moot. The default is now the new regime under Section 115BAC, and under it almost the entire chapter of deductions is switched off, no 80C, no 80D, no 80G, no 80E, no 80TTA. The only survivors are the employer's contribution to NPS and a couple of niche items, plus the standard deduction on salary.
So if you file on the default regime, the deductions below simply do not apply, however eligible you are. To claim them you must actively opt for the old regime. That is a real calculation, not a formality: an NRI with, say, home-loan principal and a life-insurance premium and some donations may be clearly better off under the old regime, while one with little to deduct is better off on the new regime's lower rates. The right move is to compute both, which is the first thing worth doing.
Under the old regime: what an NRI can claim
Choosing the old regime, an NRI gets a real but limited set. Under Section 80C you can claim life-insurance premiums, ELSS, the principal part of a home-loan repayment, and children's tuition fees, up to the ₹1.5 lakh cap. But the popular small-savings routes are closed: an NRI cannot newly open a PPF account, NSC or the five-year deposits, though a PPF opened while you were resident runs to maturity. Contributions to NPS qualify, including the extra ₹50,000.
Beyond 80C, an NRI can claim 80D for health-insurance premiums, 80G for donations, with the rule that any cash donation over ₹2,000 is disallowed, so give by bank transfer, 80TTA for up to ₹10,000 of interest on an NRO savings account, and 80E for interest on an education loan. These are the ones worth lining up if you go old-regime.
What an NRI cannot claim
Some deductions are barred to an NRI even under the old regime, because the law ties them to being resident. The ₹50,000 senior-citizen interest deduction under 80TTB is for resident senior citizens only, so an NRI cannot use it even at 60-plus, and takes the smaller 80TTA instead. The disability and serious-illness reliefs under 80U, 80DD and 80DDB all require the person, or the dependant, to be resident in India, so they are not available to a non-resident.
One more that catches people: the Section 87A rebate, which wipes out tax for smaller incomes, is only for resident individuals, so an NRI does not get it and pays tax from the first slab upward. None of this is a reason to overpay, it is a reason to file on the regime and the deductions that actually apply to you. A practising CA runs the old-versus-new comparison and claims exactly what an NRI is entitled to, no more and no less.